Characteristics of quantum-classical correspondence for two interacting spins - art. no. 052103

The conditions of quantum-classical correspondence for a system of two inte racting spins are investigated. Differences between quantum expectation val ues and classical Liouville averages are examined for both regular and chao tic dynamics well beyond the short-time regime of narrow states. We find th at quantum-classical differences initially grow exponentially with a charac teristic exponent consistently larger than the largest Lyapunov exponent. W e provide numerical evidence that the time of the break between the quantum and classical predictions scales as log(T (h) over bar), where T is a char acteristic system action. However, this logarithmic break-time rule applies only while the quantum-classical deviations are smaller than O((h) over ba r). We find that the quantum observables remain well approximated by classi cal Liouville averages over long times even for the chaotic motions of a fe w degree-of-freedom system. To obtain this correspondence it is not necessa ry to introduce the decoherence effects of a many degree-of-freedom environ ment.